Main Analysis
For our analysis, we will construct the following factor effects model for the classroom median math score.
\[y_{ijk} = μ_{..} + τ_i + β_j + (τβ)_{ij} + ε_{ ijk}\] for: \[i \in [1,2,3,4]\] \[j \in [1,2,...,76]\] Where:
\[\sum_{i=1}^{4} τ_i = 0\] \[\sum_{i=1}^{76} β_j = 0\] - \(μ_{..}\) represents the overall classroom median score across all treatment levels.
- \(τ_i\) represents the effect of each class size on the overall median math score.
- \(β_j\) represents the effect of each school on the overall median math score.
- \((τβ)_{ij}\) represents the interaction effect, if any, of each school & class size combination on the overall median math score.
I really think we should talk about the alternative, no-interaction model here.